In electronics a NOT gate is more commonly called an inverter. The circle on the symbol is called a bubble, and is used in logic diagrams to indicate a logic negation between the external logic state and the internal logic state (1 to 0 or vice versa).
A weather watch, on the other hand, typically refers to an alert issued to indicate that conditions are favorable for the development of dangerous weather patterns, although the dangerous weather conditions themselves are not currently present.
A tornado watch means that tornado development is possible. Keep a watchful eye on the sky for threatening weather and stay tuned to radio and television and listen for weather bulletins. A tornado warning means that a tornado has been sighted or indicated by radar.